Math
Lesson Plan

Not So Average Mountains

Learning Objective:
Using a data set, compare mean, media and mode.

Teacher Directions:
Seven out of ten of the highest mountains in the world can be found in Nepal. All ten are in Asia. You can find dozens of mountain peaks in the Himalayas that are taller than Mt. McKinley. You might even say that Mt. McKinley would only be an average mountain in the Himalayas.

But what does average mean? When you talk "average," you can be talking about the mean, the median or the mode. The mean is a value that is computed by dividing the sum of a set of terms by the number of terms. Median is the middle value. Half the numbers are above the median and half are below. The mode is the number that is repeated the most.

Let’s see how Mt. McKinley stacks up to the highest mountains in the world as well as the highest mountains in the Himalayas. Let’s take a look at the list of the ten highest peaks in the world.

Rank	Mountain Name	Height	Country
1	Mount Everest	8,850m (29,034ft)	Nepal/China (Tibet)
2	Qogir (K2)	8,611m (28,250ft)	Pakistan (Kashmir)
3	Kangchenjunga	8,598m (28,208ft)	Nepal/China (Tibet)
4	Makalu I	8,481m (27,824ft)	Nepal/China (Tibet)
5	Dhaulagiri	8,172m (26,810ft)	Nepal
6	Manaslu I	8,156m (26,760ft)	Nepal
7	Cho Oyu	8,189m (26,750ft)	Nepal/China (Tibet)
8	Nanga Parbat	8,126m (26,660ft)	Pakistan (Kashmir)
9	Annapurna I	8,078m (26,504ft)	Nepal
10	Gasherbrum	8,068m (26,470ft)	Kashmir

Mt. McKinley altitude is 20,320 ft. How much taller is the average of the top ten mountains taller than Mt. McKinley? In order to answer this question, what other questions will we need to answer?

Let’s get started. In order to get the average of the top ten mountains, we will need to calculate the mean. Again, the mean is a value that is computed by dividing the sum of a set of terms by the number of terms. In other words, add up the top ten and then divide by ten. That will be your mean. Next, you will need to subtract Mt. McKinley’s altitude from that mean.

Another way to answer the opinion, "Mt. McKinley is an average mountain," would be to see where Mt. McKinley would rank in comparison to the other tall peaks in the Himalayas. We might ask ourselves the following questions:

Let’s look at the list of the top 75 peaks in the Himalayas. First, let’s look at the median or middle value. There are 75 mountains on the list. What would the middle be? How does Mt. McKinley compare to that mountain?

Now let’s look at how Mt. McKinley would compare to the mode of the 75 peaks. Since each peak has an exact altitude that is different, let’s round each peak to the nearest thousand. If you do that, what is the most common altitude of the top 75? How does Mt. McKinley compare to that number?

Lastly, let’s compare Mt. McKinley’s altitude to the mean of the top 75. Use a calculator to add all 75 numbers. What do you get when you divide that number by 75? How does that number compare to Mt. McKinley?

So, is Mt. McKinley an average mountain? Why or why not?

Resources:
Top 75 Peaks of the Himalayas
Peakware World Mountain Encyclopedia

Activity Sheet:
none

Assessment:
Math Assessment Sheet*